A Penalty Method for Elliptic Variational–Hemivariational Inequalities

Autores
Sofonea, Mircea; Tarzia, Domingo Alberto
Año de publicación
2024
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We consider an elliptic variational–hemivariational inequality in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution ∈ . We associate inequality to a sequence of elliptic variational–hemivariational inequalities {} , governed by a set of constraints ̃⊃ , a sequence of parameters {}⊂ℝ+ , and a function . We prove that if, for each ∈ℕ , the element ∈̃ represents a solution to Problem , then the sequence {} converges to u as →0 . Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set ̃ and the function . The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation.
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Italia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
Materia
Penalty method
Elliptic Variational-Hemivariational inequalities
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/268980
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network_name_str CONICET Digital (CONICET)
spelling A Penalty Method for Elliptic Variational–Hemivariational InequalitiesSofonea, MirceaTarzia, Domingo AlbertoPenalty methodElliptic Variational-Hemivariational inequalitieshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We consider an elliptic variational–hemivariational inequality in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution ∈ . We associate inequality to a sequence of elliptic variational–hemivariational inequalities {} , governed by a set of constraints ̃⊃ , a sequence of parameters {}⊂ℝ+ , and a function . We prove that if, for each ∈ℕ , the element ∈̃ represents a solution to Problem , then the sequence {} converges to u as →0 . Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set ̃ and the function . The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation.Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; ItaliaFil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; ArgentinaMultidisciplinary Digital Publishing Institute2024-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/268980Sofonea, Mircea; Tarzia, Domingo Alberto; A Penalty Method for Elliptic Variational–Hemivariational Inequalities; Multidisciplinary Digital Publishing Institute; Axioms; 13; 10; 10-2024; 1-172075-1680CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/13/10/721info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms13100721info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T09:53:17Zoai:ri.conicet.gov.ar:11336/268980instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 09:53:17.601CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv A Penalty Method for Elliptic Variational–Hemivariational Inequalities
title A Penalty Method for Elliptic Variational–Hemivariational Inequalities
spellingShingle A Penalty Method for Elliptic Variational–Hemivariational Inequalities
Sofonea, Mircea
Penalty method
Elliptic Variational-Hemivariational inequalities
title_short A Penalty Method for Elliptic Variational–Hemivariational Inequalities
title_full A Penalty Method for Elliptic Variational–Hemivariational Inequalities
title_fullStr A Penalty Method for Elliptic Variational–Hemivariational Inequalities
title_full_unstemmed A Penalty Method for Elliptic Variational–Hemivariational Inequalities
title_sort A Penalty Method for Elliptic Variational–Hemivariational Inequalities
dc.creator.none.fl_str_mv Sofonea, Mircea
Tarzia, Domingo Alberto
author Sofonea, Mircea
author_facet Sofonea, Mircea
Tarzia, Domingo Alberto
author_role author
author2 Tarzia, Domingo Alberto
author2_role author
dc.subject.none.fl_str_mv Penalty method
Elliptic Variational-Hemivariational inequalities
topic Penalty method
Elliptic Variational-Hemivariational inequalities
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We consider an elliptic variational–hemivariational inequality in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution ∈ . We associate inequality to a sequence of elliptic variational–hemivariational inequalities {} , governed by a set of constraints ̃⊃ , a sequence of parameters {}⊂ℝ+ , and a function . We prove that if, for each ∈ℕ , the element ∈̃ represents a solution to Problem , then the sequence {} converges to u as →0 . Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set ̃ and the function . The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation.
Fil: Sofonea, Mircea. Université de Perpignan Via Domitia; Italia
Fil: Tarzia, Domingo Alberto. Universidad Austral. Facultad de Ciencias Empresariales. Departamento de Matemáticas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Rosario; Argentina
description We consider an elliptic variational–hemivariational inequality in a real reflexive Banach space, governed by a set of constraints K. Under appropriate assumptions of the data, this inequality has a unique solution ∈ . We associate inequality to a sequence of elliptic variational–hemivariational inequalities {} , governed by a set of constraints ̃⊃ , a sequence of parameters {}⊂ℝ+ , and a function . We prove that if, for each ∈ℕ , the element ∈̃ represents a solution to Problem , then the sequence {} converges to u as →0 . Based on this general result, we recover convergence results for various associated penalty methods previously obtained in the literature. These convergence results are obtained by considering particular choices of the set ̃ and the function . The corresponding penalty methods can be applied in the study of various inequality problems. To provide an example, we consider a purely hemivariational inequality that describes the equilibrium of an elastic membrane in contact with an obstacle, the so-called foundation.
publishDate 2024
dc.date.none.fl_str_mv 2024-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/268980
Sofonea, Mircea; Tarzia, Domingo Alberto; A Penalty Method for Elliptic Variational–Hemivariational Inequalities; Multidisciplinary Digital Publishing Institute; Axioms; 13; 10; 10-2024; 1-17
2075-1680
CONICET Digital
CONICET
url http://hdl.handle.net/11336/268980
identifier_str_mv Sofonea, Mircea; Tarzia, Domingo Alberto; A Penalty Method for Elliptic Variational–Hemivariational Inequalities; Multidisciplinary Digital Publishing Institute; Axioms; 13; 10; 10-2024; 1-17
2075-1680
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://www.mdpi.com/2075-1680/13/10/721
info:eu-repo/semantics/altIdentifier/doi/10.3390/axioms13100721
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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